Many optical systems require devices having specific optical properties, in particular, surface flatness, thickness uniformity, and/or bow. Surface flatness of an article is determined by measuring the variation of the article's surface from a specified surface profile (the profile, for example, may have a certain bow). The thickness uniformity is measured by the article's variation from a specified thickness or profile (e.g., parallel or wedge-shaped). Both of these parameters are typically measured in units of optical waves of variation from the specified profile per transverse distance, e.g., waves/cm, where the wave is a specified wavelength, e.g., of the particular light being used for measurement or for the ultimate use. When used herein, units of waves/cm indicate an average measurement over the area of the article intended to have the desired optical characteristics. Bow is a physical measurement, determined as shown by FIG. 1. The distance B from the center of an article to a line drawn between two contact points where a plane meets the article is divided by half of the distance Y of that line. The units (e.g., B cm/(Y/2) cm) divide out to give a unitless value. Methods for forming optical articles are discussed in U.S. Pat. No. 5,932,045, entitled “Methods for Fabricating a Multilayer Optical Article,” and U.S. Pat. No. 6,156,415 entitled “Method for Fabricating a Multilayer Optical Article and a System Having a Multilayer Optical Article”, both of which are incorporated by reference.
For optics applications, where one is concerned with the effect of an article on light passing through that article, physical thickness uniformity is typically not relied upon. Instead, a transmission flatness is determined by measuring the deviation of the optical path length (discussed below) from the preselected profile, and FIG. 2 shows this measurement for a configuration desired to have a uniform thickness (i.e., parallel surfaces). Transmission flatness is also presented in waves/cm, and, as known to those in the art, transmission flatness may also be expressed in rms (root mean squared) waves/cm or by the Strehl value, as discussed in J. W. Goodman, Introduction to Fourier Optics, McGraw-Hill, 1968. FIG. 2 shows two paths through a multilayer article, the paths located a distance z from each other transversely across the article. The physical path length difference across distance z is |1′−1|, and the variation from exact thickness uniformity is |1′−1|/z, which is typically measured in micrometers/cm. The physical path length is not affected by, nor does it take into account, the refractive indices of the individual layers 10, 12, and 14, or the wavelength of the light being used.
Optical path length (OPL) is the relevant parameter for transmission flatness and is represented by the following formula:
      OPL    =                            ∑                                                j            ⁢      njLj        ,where                nj is the refractive index of layer j and        Lj is the physical path length through layer j.        
In contrast to physical path length, the OPL depends on the refractive index. For example, in a multilayer article such as that of FIG. 2, the OPL depends on the refractive indices of layers 10, 12, and 14. Specifically, the OPL difference (ΔOPL) across the article of FIG. 2 is equal to:|(n10L10+n12L12+n14L14)−(n10L′10+n12L′12+n14L′14)|
This equation shows that where the goal is a small OPL difference, if the substrates have relatively large individual thickness variations, but the overall thickness variation is relatively small, it is useful for the refractive indices of the substrates to be close. As reflected in FIG. 2, the transmission flatness, assuming a parallel configuration is desired, is therefore ΔOPL/z. For optics applications, it is clear that the variation from a selected profile in OPL is more meaningful than the change in physical path length per transverse unit.
Transmission and surface flatness values are presented in waves/cm, where the value given is for a specified wavelength. Use of such waves/cm herein indicates that the value is for the optical path length as opposed to the physical path length. For purposes of the present application, values in waves/cm are useful at least for wavelengths ranging from about 0.3 to about 0.9 micrometers, but the concept of the invention extends beyond this range.
For substrates typically used in optics applications, there are three basic types of thickness variations that affect surface and transmission flatness. The first type is a linear thickness change from low to high over the surface of the substrate, whereby the substrate essentially takes the form of a wedge. The thickness variation of such a substrate per unit length is relatively constant. The second type of a variation is a gradual, wavy, or random, variation, where the thickness varies, for example, from low to high to low to high gradually across the width of the substrate. The thickness variation of such a substrate per unit length is relatively constant, but the substrate does not take the form of a wedge. The third type of variation is localized, sharp divots or peaks. Such divots or peaks typically cause rapid variations in thickness measurements taken at different locations along a substrate and may therefore skew an rms measurement. Structures having this third type of variation are typically measured in terms of scratch and dig, as known in the art. Clearly, these characteristics often cause numerous difficulties when attempting to form structures with combinations of low surface smoothness variations, low thickness uniformity variations, and/or low bow.
Articles used in precise applications desirably have a surface and transmission flatness of 0.1 waves/cm or better. Articles for transmission applications where parallel surfaces are desired desirably have a bow of 10−2 or less (less meaning numerically smaller), and articles for reflection applications where parallel surfaces are desired desirably have a bow of 10−5 or less. It is difficult to prepare or obtain substrates or multilayer articles having such properties. High quality glass intended for flat panel displays (referred to herein as display glass), for example, will have surface and transmission flatness values ranging from about 0.25 to about 4 waves/cm. To obtain better, and more consistent flatness values, it is necessary to obtain a thick piece of glass and polish the glass to a desired flatness. Such chemical/mechanical polishing, however, is expensive and time-consuming, and may still be inadequate for preparing substrates and articles having the above properties. Easier and less expensive methods for improving the optical flatness of substrates and for forming optical articles, e.g., articles, having certain bow, thickness uniformity, and surface flatness, are desired, particularly for optical articles which have already been previously formed with inadequate surface flatness, thickness uniformity, or bow.
It is also possible for cells made according to the invention to be used for holographic storage. Memory cells for holographic data storage systems are discussed, for example, in H.-Y. Li et al., “Three-dimensional holographic disks,” Appl. Opt., 33, pp. 3764–3774 (1994), and A. Pu et al., “A new method for holographic data storage in photopolymer films,” Proceedings from IEEE/IEOS 1994 Symposium, pp. 433–435, the disclosures of which are hereby incorporated by reference. It is desirable for the cells to have a surface and transmission flatness of about 0.25 waves/cm or better and a bow of about 10−2 or less. Conventional methods of disposing photopolymers between substrates do not provide these properties. Thus, there has been a need for holographic memory cells that have these properties. In addition, there has been a need for memory cells for holographic data storage systems with increased storage capacity.